EQUILIBRIUM OF RIGID BODIES 45 a — h From the figure we obtain cos a = a therefore sin a = - \/h (2 a — h), W and F = — Vh(2a-h). a FIG. 35. Since cos 6 = 0 the first equation of equilibrium gives R — W cos a DISCUSSION. — It will be observed that the first two of the equations of equilibrium are sufficient to solve the problem. When h is zero, F = 0 and R = IF. On the other hand when h = a, F = W and R = 0. PROBLEMS. 1. Prove that the true weight of a body is the geometric mean between the apparent weights obtained by weighing it in both pans of a false balance. 2. A uniform bar weighing 10 pounds is supported at the ends. A weight of 25 pounds is suspended from a point 20 cm. from one end. Find the pressure at the supports if the length of the bar is 50 cm. 3. A uniform rod which rests on a rough horizontal floor and against a smooth vertical wall is on the point of slipping. Find the reactions at the two ends of the rod.